What is the sum from n=0 to infinity of n^2(1/3)^n ?

The sum from n=0 to infinity of n^2(1/3)^n is converges

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sum from n=0 to infinity of n^2(1/3)^n

n = 0 \sum \infty n^{2} (\frac{1}{3})^{n}

converges

Solution steps

n = 0 \sum \infty n^{2} (\frac{1}{3})^{n}

Apply Series Ratio Test:

converges

= converges

\int e^{- s t} t^{5} d t

f^{^{'}} (x) = \frac{1}{3 x ^{\frac{2}{3}}}

\int \frac{3}{56} x^{2} d x

y = 7 (x^{3} + x^{2}) \frac{2}{3}

\frac{d}{d x} (10 (1. 1^{\frac{x}{2}}))

What is the sum from n=0 to infinity of n^2(1/3)^n ?
The sum from n=0 to infinity of n^2(1/3)^n is converges